Exciton Dynamics, Transport, and Annihilation in Atomically Thin Two

Jun 29, 2017 - transport, and annihilation in 2D TMDCs. Intrinsically, dark and bright exciton energy splitting is likely to play a key role in modula...
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Exciton Dynamics, Transport, and Annihilation in Atomically Thin Two-Dimensional Semiconductors Long Yuan, Ti Wang, Tong Zhu, Mingwei Zhou, and Libai Huang* Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States ABSTRACT: Large binding energy and unique exciton fine structure make the transition metal dichalcogenides (TMDCs) an ideal platform to study exciton behaviors in two-dimensional (2D) systems. While excitons in these systems have been extensively researched, there currently lacks a consensus on mechanisms that control dynamics. In this Perspective, we discuss extrinsic and intrinsic factors in exciton dynamics, transport, and annihilation in 2D TMDCs. Intrinsically, dark and bright exciton energy splitting is likely to play a key role in modulating the dynamics. Extrinsically, defect scattering is prevalent in single-layer TMDCs, which leads to rapid picosecond decay and limits exciton transport. The exciton−exciton annihilation process in single-layer TMDCs is highly efficient, playing an important role in the nonradiative recombination rate in the high exciton density regime. Future challenges and opportunities to control exciton dynamics are discussed.

A

close-lying spin-allowed bright and spin-forbidden dark exciton levels.12,15−19 Exciton dynamics in monolayer TMDCs have been extensively studied;20−27 however, the interpretation of these measurements varies with exciton lifetime ranging from a few picoseconds to nanoseconds.26 Dark and bright exciton states are expected to play a key role in the dynamics of the 2D excitons;17,28 however, how such exciton fine structure affects dynamics is not fully addressed in the current literature. Because the dark states could lie either above or below the bright states depending on the materials,16,28 the lack of understanding of the dark states is likely one of the reasons for the widespread of exciton lifetimes measured. For instance, timeresolved photoluminescence (PL) spectroscopy and transient absorption (TA) spectroscopy, the two most widely used tools to study exciton dynamics, could be sensitive to different exciton populations. Both experimental and theoretical efforts to address the dynamics of dark and bright excitons will be necessary for realizing electronic and optoelectronic applications of TMDCs. In addition, there currently lacks a comprehensive understanding of exciton transport in the TMDCs materials. It will be useful to establish the intrinsic limit of exciton transport, which is highly relevant for applications such as photovoltaics. Previous reports on exciton transport have shown contradicting results: the exciton diffusion coefficient is higher for single layer than for bulk WSe229 but the opposite is true for MoSe2.30 In this Perspective, we discuss the intrinsic and extrinsic factors that control exciton dynamics and transport in 2D TMDCs. This Perspective is not meant to be a comprehensive

tomically thin and two-dimensional (2D) transition metal dichalcogenides (TMDCs) are layered structures where adjacent layers are held by van der Waals force.1 Because the interlayer coupling is relatively weak, the electrons and holes are confined in the layer plane. Bound electron−hole pairs, or excitons, dominate the optical properties of these materials.2,3 Recent experimental measurements showed that the exciton binding energy is in the range of 0.3−0.7 eV for the TMDCs monolayers, more than an order of magnitude larger than other previously investigated 2D excitonic structures such as semiconducting quantum wells.4−6 These 2D excitons are neither strictly Wannier nor Frenkel type, but have exciton radii (∼2 nm)6 in the intermediate regime. The stable excitons at room temperature make the TMDCs an ideal platform to study exciton behaviors in 2D systems.

Exciton fine structure in monolayers of TMDCs results from strong spin−orbit coupling, broken inversion symmetry, and quantum confinement effects. Exciton fine structure in monolayers of TMDCs results from strong spin−orbit coupling, broken inversion symmetry, and quantum confinement effects. As the number of layer reduces to single layer, the band structure of TMDCs undergoes indirect-to-direct band transition.2,3,7,8 Valence band edge splits into two spin-polarized bands at inequivalent valleys (K/K′) in the Brillouin zone due to strong spin−orbit coupling effect,9 which has an energy difference of a few hundred millielectronvolts.10−14 Spin−orbit coupling also leads to a splitting in the conduction band, albeit much smaller, from several millielectronvolts to tens of millielectronvolts, leading to © 2017 American Chemical Society

Received: April 12, 2017 Accepted: June 29, 2017 Published: June 29, 2017 3371

DOI: 10.1021/acs.jpclett.7b00885 J. Phys. Chem. Lett. 2017, 8, 3371−3379

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Figure 1. (a) Schematic illustration of a 1L-WS2 layer on a substrate. (b) Schematic drawing of the band structure of 1L-WS2 and multilayer WS2, with arrows indicating A, B, C, and I excitons. Solid lines denote direct excitons, and the dashed line corresponds to the indirect exciton. (c) Optical micrograph of a 1L-WS2 flake on a Si/SiO2 substrate. (d) Differential reflection and PL spectra of a 1L-WS2 flake.

Figure 2. (a) Summary of literature-reported bright-dark exciton energy splitting for TMDC monolayers, including both experimental and theoretical values.12,15−18 (b) Schematic illustration of the spin allowed bright exciton (AB) and spin forbidden dark exciton (AD) in W-based TMDCs at the K and K′ valleys. Δc is the bright-dark exciton energy splitting. (b) Kinetic model for the dynamics of the bright and dark excitons. (c) Comparison of temperature dependence of the time-integrated PL intensity of WSe2 and MoS2. Adopted from ref 17 with permission. Copyright 2015 American Physical Society. (e) Temperature-dependent PL lifetime from a suspended monolayer of WSe2. Adopted from ref 17 with permission.

review of the large volume of literature on exciton dynamics, but instead we focus on the following properties that are critical to understand 2D excitons in TMDCs. First, we discuss how the equilibrium between the bright and dark exciton populations affects exciton lifetimes. Second, we address how the environmental factors, such as defects, impact the dynamics and transport of the excitons. Finally, we examine exciton−exciton annihilation process, which could play an important role in determining nonradiative recombination rate in the high exciton density regime. Bright and Dark Exciton Structure and Dynamics. Recent evidence for the existence of the spin-forbidden dark excitons16,17

suggests that they will be critical in understanding exciton dynamics. For instance, the relaxation to the dark exciton levels has been found to be important for systems such as singlewalled carbon nanotubes.31−33 In the following, we summarize the current literature on bright and dark exciton dynamics and discuss how the population equilibrium between the bright and dark states could affect exciton lifetime. Direct optical transitions occur at the K and K′ points of the Brillouin zone, leading to the formation of both A and B excitons (Figure 1b) in TMDCs. Figure 1 shows a typical exfoliated single-layer WS2 (1L-WS2), whose reflective spectrum exhibits 3372

DOI: 10.1021/acs.jpclett.7b00885 J. Phys. Chem. Lett. 2017, 8, 3371−3379

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following two coupled rate equations:

three excitonic transitions (labeled as A, B, and C). The valence bands near the K and K′ points are contributed mainly by the dx2−y2 and dxy orbitals of metal atoms in TMDCs. The energy difference (380 meV) between A and B exciton transition is due to the large spin−orbit splitting in the valence band.8 The C exciton has been ascribed to the band nesting effect.21 When the thickness increased to two layers or thicker, an indirect exciton (I) is form between the K and Λ points. The PL emission peak near 620 nm (2 eV) corresponds to the direct interband recombination of the A exciton of 1L-WS2 (Figure 1d).8 The conduction bands near the K and K′ points are mainly from the dz2 orbitals of metal atoms, and no splitting is expected when considering only the dz2 orbitals.12 However, the chalcogen orbitals and higher order couplings to other orbitals of metal atoms also play a role, leading to a spin splitting of 10s meV in the conduction bands. Because of the competition between these two effects, the sign of this conduction band splitting differs among the different TMDCs.16,17 For WX2 (X = S, Se, Te), the lowest energy exciton is a dark state. For MoSe2 and MoTe2, on the other hand, electrons in the conduction band minimum (CBM) are expected to have the same sign polarization with holes in the valence band maximum (VBM), leading to a bright state as the lowest exciton energy level.19,34 The case for MoS2 is currently under debate: some concluded that the bright exciton is the lowest level with a small splitting of a few millielectronvolts,12 while other inferred a dark exciton with energy as much as ∼100 meV below the bright exciton.18 The conduction band splitting Δc for different TMDC materials is summarized in Figure 2a.12,15−18 Because of the splitting in the conduction band, there are two intravalley bright (singlet-like) excitons (AB) and two intravalley spinforbidden (triplet-like) “dark” excitons (AD), as schematically depicted in Figure 2b, one of each at the K and K′ valleys.16,17 There are also four additional intervalley dark excitons.17 Zhang et al. first experimentally verified the existence of the dark exciton states in WSe2 using temperature-dependent steady-state and time-resolved PL measurements.17 The population of AB and AD (NAB and NAD) obey the Boltzmann distribution as given by

NAB NAD

d NA

B

dt d NA

D

dt

= −kBNAB − k1NAB + k −1NAD

(1)

= −kDNAD − k −1NAD + k1NAB

(2)

where kB(D) is the relaxation rate of the bright (dark) state to the ground state, and k1(−1) is the rate for converting from the bright (dark) to the dark (bright) state. k1 and k−1 are related k

by population equilibrium as given by k−1 = 1

NAB

NAD

= e−Δc / kbT .

When k1, k−1 ≫ kB ≫ kD, the solution can be simplified to NAB ∼ e−(k1+ k−1)t +

k −1 −(kD+ k−1kB/ k1)t e k1

NAD ∼ − e−(k1+ k−1)t + e−(kD+ k−1kB/ k1)t

(3) (4)

Therefore, the population dynamics of the bright state should consist of two exponential decays, while there is an exponential rise and an exponential decay for the dynamics of the dark state. Recently, a similar rate equation model has been applied to explain the variation in the observed degree of circular polarization of the PL emission in different TMDCs monolayers, suggesting subpicosecond relaxation from the bright to the dark state.19 The fast relaxation from the bright to the dark exciton level in WSe2 can also be inferred by the temperature-dependent PL lifetime measurements by Zhang et al., which showed that the fast decay component (600 nm. The spatial extent of exciton for the monolayer has been estimated to ∼2 nm.6 This large interexciton distance implies that exciton diffusion as discussed in the last section has to occur before exciton annihilation.53 The following kinetic scheme describes the two rate-determining steps: (1) the diffusion of two excitons toward each other; (2) the annihilation of the two excitons when they are sufficiently close to each other with rate.

In bilayer and trilayer WS2, only a fraction of exciton encounters results in annihilation. thin TMDCs is, overall, 1 order of magnitude higher than that in 2D quantum wells (∼10−3 cm2s−1).59 The efficient exciton−exciton annihilation in 1L-WS2 implies that the inverse process, impact ionization (multiple exciton generation),60 could also be effective. By following the method used to obtain the Auger recombination time in quantum dots,50 we extract the exciton−exciton annihilation time to be ∼400 ps in monolayer at an initial exciton density of 1.6 × 109 cm−2.51 Such slow exciton−exciton annihilation on the hundreds of picoseconds time scale makes it quite possible to extract the addition exciton generated. In summary, TMDCs with large exciton binding energy and unique exciton fine structure provide a model system for investigating 2D excitons. This perspective focuses on the intrinsic and extrinsic factors that affect exciton dynamics, transport, and annihilation. We stress here the importance of the dark exciton levels in controlling intrinsic exciton relaxation dynamics. To extract the correct exciton radiative and nonradiative lifetimes, it will be important to take into account the dark-bright exciton splitting. This is an important open question for the field that requires future works on TMDCs with different bright-dark exciton splitting to provide a comprehensive understanding of exciton dynamics for these important materials. Excitons in TMDCs are intrinsically very mobile with phononlimited exciton diffusion constant is around 10 cm2s−1. However, defect scattering limits exciton mobility in single-layer TMDCs, with scattering times as short as 2 ps. As a result, exciton mobility is highly dependent on sample quality and fabrication methods, showing orders of magnitude difference for exfoliated and CVD grown samples. To realize applications, it will be critical to further develop ways to control defects in these materials. Exciton−exciton annihilation process in single-layer TMDCs is highly efficient, 2 orders of magnitude higher than that in 2D quantum wells. Such efficient exciton−exciton annihilation suggests potential multiple exciton generation in these materials, which warrants further investigation. Sample Preparations. Single-layer and multilayer WS2 with different thicknesses were mechanical exfoliated from commercial bulk WS2 crystals (2D Semiconductor). CVD-WS2 was obtained from 2D layers. We used PL spectroscopy and atomic force microscopy (AFM) to identify the thickness of WS2 layers. Transient Absorption Microscopy (TAM). Exciton dynamics and propagation measurements in WS2 with different thickness were performed by a home-built TAM system. A Ti:Sapphire oscillator (Coherent Mira 900) pumped by a Verdi diode laser (Verdi V18) was used as the light source (output at 790 nm, 80 MHz repetition rate). 70% of the pulse energy was fed into the optical parametric oscillator (Coherent Mira OPO) to generate probe light at a range of 600 to 640 nm, while the remainder 30% was doubled to 395 nm and serves as the pump beam. The pump beam was modulated at 1 MHz using an acoustic optical modulator (model R21080-1DM, Gooch & Housego). A 40×/NA = 0.60 objective was used to focus the laser beams onto the sample, and the transmission light was then collected by an optical condenser and detected by an

ka

E + E ⇄kkdiffusion (EE) → E(higher energy) dissociate

where E is an isolated exciton, (EE) denotes exciton pair sufficiently close that annihilation can take place, and ka is the annihilation rate proceeding from (EE). kdiffusion is defined as the rate of change of the number of the close pair per unit area and kdissociate is rate for the reverse process. The overall exciton− exciton annihilation rate becomes γ=

kdiffusionka kdissociate + ka

(9)

Overall, the exciton diffusion rate is at least an order of magnitude faster than the overall exciton−exciton annihilation rate (kdiffusion ∼ kdissociate ≫ ka), therefore ka is the rate-limited step (i.e., γ ∼ ka). Exciton diffusion rate is even higher in the 2L-WS2 and 3L-WS2 than in the 1L-WS2, as shown in Figure 5. Thus, the much reduced γ values measured in the 2L-WS2 and 3L-WS2 must be due to smaller values of ka. We explain thickness dependence of ka as follows.51 First, at the single-layer limit, stronger Coulomb interaction between the electrons and holes leads to stronger many-body interaction. As presented in the discussion of the dark and bright exciton dynamics, the dark excitons could contribute significantly to the PL dynamics shown in Figure 6 for the 1L-WS2. Recent theoretical calculations that show Auger recombination can be very efficient out of the dark states.54 Second, exciton−exciton annihilation requires conservation of both energy and momentum. For the 2L-WS2 and 3L-WS2, which are indirect semiconductors, momentum conservation requires assistance from phonons.55,56 On the contrary, for the direct bandgap monolayer, the involvement of phonons is not necessary. The additional requirement for phonon assistance makes exciton−exciton annihilation a much less probable event, leading to at least 2 orders of magnitude smaller γ in bilayer and trilayer than in monolayer. In other words, in bilayer and trilayer WS2, only a fraction of exciton encounters results in annihilation. These results also show that the exciton−exciton annihilation rate does not necessary reflect the diffusion constant, and exciton annihilation is not a reliable way to measure diffusion. Other single-layer TMDCs exhibit similar exciton−exciton annihilation rates.53,57,58 Mouri et al. determined the exciton− exciton annihilation rate to be ∼0.35 cm2 s−1 in 1L-WSe2.53 Kumar et al. measured the exciton−exciton annihilation rate in 1L-MoSe2 to be ∼0.33 cm2s−1 by using ultrafast pump−probe spectroscopy.58 The exciton−exciton annihilation in atomically 3377

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(2) Mak, K. F.; Lee, C.; Hone, J.; Shan, J.; Heinz, T. F. Atomically Thin MoS2: A New Direct-Gap Semiconductor. Phys. Rev. Lett. 2010, 105, 136805. (3) Splendiani, A.; Sun, L.; Zhang, Y.; Li, T.; Kim, J.; Chim, C. Y.; Galli, G.; Wang, F. Emerging photoluminescence in monolayer MoS2. Nano Lett. 2010, 10, 1271. (4) He, K. K. N.; Zhao, L.; Wang, Z.; Mak, K.; Zhao, H.; Shan, J. Tightly Bound Excitons in Monolayer WSe2. Phys. Rev. Lett. 2014, 113, 026803. (5) Chernikov, A.; Berkelbach, T. C.; Hill, H. M.; Rigosi, A.; Li, Y.; Aslan, O. B.; Reichman, D. R.; Hybertsen, M. S.; Heinz, T. F. Exciton Binding Energy and Nonhydrogenic Rydberg Series in Monolayer WS2. Phys. Rev. Lett. 2014, 113, 076802. (6) Stier, A. V.; McCreary, K. M.; Jonker, B. T.; Kono, J.; Crooker, S. A. Exciton diamagnetic shifts and valley Zeeman effects in monolayer WS2 and MoS2 to 65 T. Nat. Commun. 2016, 7, 10643. (7) Arora, A.; Nogajewski, K.; Molas, M.; Koperski, M.; Potemski, M. Exciton band structure in layered MoSe2: from a monolayer to the bulk limit. Nanoscale 2015, 7, 20769. (8) Zhao, W.; Ghorannevis, Z.; Chu, L.; Toh, M.; Kloc, C.; Tan, P.H.; Eda, G. Evolution of Electronic Structure in Atomically Thin Sheets of WS2 and WSe2. ACS Nano 2013, 7, 791. (9) Xiao, D.; Liu, G.-B.; Feng, W.; Xu, X.; Yao, W. Coupled Spin and Valley Physics in Monolayers of MoS2 and Other Group-VI Dichalcogenides. Phys. Rev. Lett. 2012, 108, 196802. (10) Ramasubramaniam, A. Large excitonic effects in monolayers of molybdenum and tungsten dichalcogenides. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 86, 115409. (11) Gong, Z.; Liu, G.-B.; Yu, H.; Xiao, D.; Cui, X.; Xu, X.; Yao, W. Magnetoelectric effects and valley-controlled spin quantum gates in transition metal dichalcogenide bilayers. Nat. Commun. 2013, 4, 2053. (12) Kormányos, A.; Burkard, G.; Gmitra, M.; Fabian, J.; Zólyomi, V.; Drummond, N. D.; Fal’ko, V. k·p theory for two-dimensional transition metal dichalcogenide semiconductors. 2D Mater. 2015, 2, 022001. (13) Liu, G.-B.; Shan, W.-Y.; Yao, Y.; Yao, W.; Xiao, D. Three-band tight-binding model for monolayers of group-VIB transition metal dichalcogenides. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 88, 085433. (14) Kormányos, A.; Zólyomi, V.; Drummond, N. D.; Burkard, G. Spin-Orbit Coupling, Quantum Dots, and Qubits in Monolayer Transition Metal Dichalcogenides. Phys. Rev. X 2014, 4, 011034. (15) Qiu, D. Y.; Cao, T.; Louie, S. G. Nonanalyticity, Valley Quantum Phases, and Lightlike Exciton Dispersion in Monolayer Transition Metal Dichalcogenides: Theory and First-Principles Calculations. Phys. Rev. Lett. 2015, 115, 176801. (16) Echeverry, J. P.; Urbaszek, B.; Amand, T.; Marie, X.; Gerber, I. C. Splitting between bright and dark excitons in transition metal dichalcogenide monolayers. Phys. Rev. B: Condens. Matter Mater. Phys. 2016, 93, 121107. (17) Zhang, X.-X.; You, Y.; Zhao, S. Y. F.; Heinz, T. F. Experimental Evidence for Dark Excitons in Monolayer WSe2. Phys. Rev. Lett. 2015, 115, 257403. (18) Molas, M. R.; Faugeras, C.; Slobodeniuk, A. O.; Nogajewski, K.; Bartos, M.; Basko, D. M.; Potemski, M. Brightening of dark excitons in monolayers of semiconducting transition metal dichalcogenides. 2D Mater. 2017, 4, 021003. (19) Baranowski, M.; Surrente, A.; Maude, D. K.; Ballottin, M.; Mitioglu, A. A.; Christianen, P. C. M.; Kung, Y. C.; Dumcenco, D.; Kis, A.; Plochocka, P. Dark excitons and the elusive valley polarization in transition metal dichalcogenides. 2D Mater. 2017, 4, 025016. (20) Korn, T.; Heydrich, S.; Hirmer, M.; Schmutzler, J.; Schueller, C. Low-temperature photocarrier dynamics in monolayer MoS2. Appl. Phys. Lett. 2011, 99, 102109. (21) Kozawa, D.; Kumar, R.; Carvalho, A.; Kumar Amara, K.; Zhao, W.; Wang, S.; Toh, M.; Ribeiro, R. M.; Castro Neto, A. H.; Matsuda, K.; Eda, G. Photocarrier relaxation pathway in two-dimensional semiconducting transition metal dichalcogenides. Nat. Commun. 2014, 5, 4543.

avalanche photodiode (Hamamatsu C5331-04). The change in the probe transmission (ΔT), induced by the pump, was detected by a lock-in amplifier (HF2LI, Zurich Instrument). For transient the dynamics scan, the pump beam and probe beam were overlapped spatially, and a mechanical translation stage (Thorlabs, LTS300) was used to delay the probe with respect to the pump. A two-dimensional galvanometer scanner (Thorlabs GVS012) was used to scan the probe beam relative to the pump beam in space to obtain the exciton diffusion profiles.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Libai Huang: 0000-0001-9975-3624 Notes

The authors declare no competing financial interest. Biographies Long Yuan is currently a Ph.D. candidate in the Department of Chemistry of Purdue University. He received his M.Sc. from the University of Science and Technology of China. His current research interests include exciton dynamics and transport in two-dimensional semiconductors using ultrafast transient absorption microscopy. Ti Wang is currently a postdoctoral associate in the Department of Chemistry at Purdue University. He received his Ph.D degree from Wuhan University, China. His current research focuses on carrier transport in two-dimensional semiconductors and perovskite materials by ultrafast transient absorption microscopy. Tong Zhu is a Ph.D. candidate in the Department of Chemistry at Purdue University. She received her B.S. degree from Harbin Institute of Technology, China. She is looking forward to receiving her Ph.D. degree in the summer of 2017. Her current research interests focus on imaging Frenkel exciton transport in molecular systems as well as studying charge and energy transfer at organic−inorganic van der Waals heterostructures using ultrafast pump−probe microscopy. Mingwei Zhou is currently an undergraduate student in the Department of Chemical Engineering of Purdue University. He currently studies optical properties of two-dimensional semiconductors. Libai Huang is currently an Assistant Professor in the Department of Chemistry at Purdue University. She received her B.S. from Peking University in 2001 and her Ph.D. from the University of Rochester in 2006. She joined the Purdue faculty in 2014. Her research program is aimed at directly imaging energy and charge transport with femtosecond time resolution and nanometer spatial resolution to elucidate energy and charge transfer mechanisms.

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ACKNOWLEDGMENTS We acknowledge the support from the National Science Foundation under Grant Number 1433490 for sample fabrication and from the U.S. Department of Energy, Office of Basic Energy Sciences, through Award DE-SC0016356 for optical measurements.

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REFERENCES

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DOI: 10.1021/acs.jpclett.7b00885 J. Phys. Chem. Lett. 2017, 8, 3371−3379